Sometimes people say that water is removed from clothes in a spin dryer by wtad7(2-vd+l- 34wx/ oerhr ae z e;6ahv;epccentrifugal force throwing the water outward. What is wrong with3wde;(hex -d/;vro r+ ep7 h4av6-z2 eaw ctal this statement?

Will the acceleration of a car be the sawo:.ht oguzf7*c8 7vo me when the car travels around a sharp curve at a constant 60 km/h as when it travels arouno7o*w 8o vz7u. :gchftd a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hil fcw1 j(gu7g+xly road. Where does the car exert the greatest and least x(1 g+7jf gwcuforces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a ch4 mqo7*pmk)jbild riding a horse on a merry-go-round. Which of these forces prov b 4op)*7kmjqmides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spilli. kq26mrsq t+q+sy f9sng out, even at the top of the circle when the bucket is upside dows 6k f+9sqqr+.sy tqm2n. Explain.

How many “accelerators”mlragi.y r ;7zv g-,a9 do you have in your car? There are at least three controls in the car which can be used to cause the car to acceleratg-m,zragiyl;7 v.ar 9e. What are they? What accelerations do they produce?

A child on a sled come3vz,8jpoi:pnt4f . pys flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain py.tj: 3p8,f4pozvnithis decrease using Newton’s second law.

Why do bicycle riders lean inward lz 1mqy;7 -mn .*hzo cue3wao.when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you ikc ur.,dh jc5*/ 4luccompute the banking angle given its speed and radius o*cjh.54cu uckl/rdi, f the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.sqn4 /. qq)icr She wants to let go at precisely the right time so thatci r)q4 qn.s/q the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitatd0,x1pjq9ik mwrr/ k:ional force on the Earth? If so, how large a force? Consider an apple rqk:i,/ 9xkdwmj01pr
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon6 exnbdqd/)x)1k mj( ,q runil v6q/j1’s orbit emnx,d /brvkq66j(1iquqdl1jn/) x)be different?

Which pulls harder gravitationally, the Earth on the Mos1bpzh by5 ou4i-df .9on, or the Moon on the Earth? Wo-.dpb4 uiz5f1h s9b yhich accelerates more?

The Sun's gravitational pull7h6w82 du7 xwjyzr8d;- wzg yl on the Earth is much larger than the Moon's. Yet the Moon's is mainl7wj7dw 2y6-8gxzhl dzw8u r;y y responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatorol*,o/0j .ax)x r wlki or at the poles? What two effects are atlo.*0xo ij/ )lkrwx,a work? Do they oppose each other?

The gravitational force on the Moo b7lc vjle2r9,n due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from therle9 7cvl,j 2b Earth?

Is the centripetal accel 1tdtij, b9v7geration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of 71digttjv ,b9the Earth?

Would it require less speed to launch a sateu;xi2bkk8m**-y xf2yy. ts qlllite (a) toward the east or (b) toward the t m ;ykf2yxs*.uxiqb2y lk8-*west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as meauvax;-q 4e ;k*k(x xjbsured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weiexka* x q-u(xvj4;;b kght be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could,8ew2l(mid:t s :gzesok 7si9 be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how2eoz:e7i(lg ms ,d w:9 8tksis objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner uzerh5 w19)1u/l;o t 5wd2 esdty;tsoexperiences “free fall” or “apparent weightlessness” between stedw t9wu1oesh l )to d uy;25s/15rzte;ps.

The Earth moves faster in its orbit around the Sun in January than in July. Is p ee/v(ab2,*g +9at csy jl1 9vkuy/rcthe Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in pv9evsb9 g(t*c/kae12y y la/c +rju,producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Exb c3z;5y ;w*qb/atbklplain how this discovery enab;zcbqy/3 bbka5;w l*t led an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. x+t3 jxw4sno1Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of jx t31 wnoxs4+ 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling zymix a2rp.8. 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its3 gae2y jbr5y4 orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the 2a3gbje4 y5r yEarth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniea6lck-tcgvcbfaj.n684y-hu y z .cl w6:+;dformly in a horizontal circle (at arm’s lengtvf. c: +ztha6nldk;l6-a 84ue6wy-. ybcgcc jh) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface9.q eleapim bz9es8c12o)*gi, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle iige1o.zq2p9 sm a8e blice9*)n its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitud5p:yt hz iz9(2fnicu4d lc+w3urxi(( e of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per min :rtzi5c2f(ci ixupnzud h+y34w l(9 (ute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is /t469qhb tpacuzp .3z revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0ubzpa9t q64h zp/ 3.ct0 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car canmls6-0w+omkqmm58ln hx)ay) 0 ;jkvq round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the hqkym ml 5j0 6wm vxq)+-nma;ko80)lscar?   

  How large must the coefficient of static friction be between the tires and the rx*b0j dwk(c;wny2k1qon7y l0 ugiz(.oad if a car is to round a level curve of radius 85 m atd7z0((k. nc 1n2wk;ojxb gy0qwl yi*u a speed of 95km/h ?   

  A device for trainins83jqd.2uuarveb/c 3z lu1 .a g astronauts and jet fighter pilots is designed to rotate a trar c3./j vubqd1 eu2l3u8za .asinee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rota :gb,lcyj+ss2q )z 9dating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turs+)2yj,az glb9q:cs dntable?   

  At what minimum speed must a roller coaster be traveling when upsi op1mh27yff-m de down at the t2of-p yh7fmm1 op of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the round8n,arz , kc9s,k2 ,aiiw7m bzxc*nn i7ed top of a hill ( ,aik*nb,nns89,kr2cm7, 7xzi caz wiradius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel zv5-kbwq j0w9 need to make for the passengeqw-w9 0v5jk bzrs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radivez)(:jq lnnx8 (w: ncus 1.10 m. At the lowest point of its motl( wq:n( nen:j8c)xz vion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the hnj f2(un5e0qy;/ beh axis of rotatio 50h2yhueeb;qf j( nn/n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled 5giz2oek1u 3u"room.g32k o izuu5e1" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass Md --hlj r0 cn1wyqqd3/ ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throurqn- c0j1w-ly3 dhq/dgh a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, bydo ,j.;d,lc7d-ew fnn not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find th.njco7 f dw-d,lde;,ne magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m a. ly z3:qp* nfap,4nois perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massezlnl1 a;5rk d(cl9 va1s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically wf1jgbsm:j) 7:ea5lr at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal com/rn, cjg sjn00b 5ib0;/9kfgnnw1r bu ponents of the net force exerted on the car (by th 9i/nb1b,rrng0n/;5 jg bsncj0uw f 0ke ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, gobli dq0afj:ui a9/8s1 qdj6 )ting from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car w0 l:uqd )ifsd j9j i68qa/tb1ahen it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a parti lruzy:vf51*wcular instant, iu frl1z5*v :wyts acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,u/ gsv2 axy/ -zps:vw3800 km (2 Earth radii) above the Earth’s surface if its mass sas gpz/v2v y3:x-uw/is 1350 kg.   

  At the surface of a certain planet, the gravqtv: . z q/-qtmcmp(n(itational acceleration g has a magnitude of 12 m/qq mmzc t(-p /(t:vq.ns$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on tz,1 ba;c1+ j-uyq xg4vj)wyw/-gkg bzhe Moon. The Moon's radius is 1.74jk1zagz4wjq1c-;gw,ygy/b+ vu) x b - $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hpu b+ da-i,0 9gr5r t4pji1puj*)rknias a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity nu)kp *u 4b9 rd ,1jnjpp+iitr5-rg0 iaear its surface?   

  A hypothetical planet has a mass 1.66 times (4nnsf ot1f4e that of Earth, but the same radius. What is g near its surfte(4fon fs14n ace?   

  Two objects attract each other gravitationally wiy rb,n y.w 2ul3 6mrceb(nr49sth a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3g9d ;z-ikp9f),fosru)0 u fmg200 m9)ugz 9ir0u,-fmp) ko;s gfd f    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frowm lgo)ozw 8y28)5fkbm the Earth’s center to a point outside the Earth where thegravitational accelerat2) )8kw bywl5m8oozg fion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has z pzbwl.-lgg 5n8x2t2y3z p/sfive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this mozzgbp28t nxy2 z/lw.s3- 5gplnster.    $\times10^12$

  A typical white-dwarf star, which once was an gq ,d,- n)cikcaverage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of i n)ck ,-gd,cqour Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weighh/p f7qvu6gd bo-a//8q* rtggtless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleratiofg*oa7d8/ thpg6 /qqr ugb /-vn of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcww+ n1(e(h9ateci )x9t4l rhkulate the magnitud9k9w 1)ttnh+ac exwrhel(i4 (e and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetskm)cfd1 z; * t*p dff9dr.oki- line up on the same side of the Sun. Calculate the total force on the Ear-m1d)o*fcfpzkd*ir ;.t 9fk dth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration ow; xpj6j7h )uxf gravity at the surface of Mars is 0.38 of what it is on Earth, and that M;7x)6xjjuwp hars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value18jen ds.bbhw k/z:2 p for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained nkd8bhs2 /zbw:1.pje using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of ,my.c3+ a2dwrcfy7me a satellite moving in a stable circular orbit about the Earth at acmcw,7 mre3f .d y2ya+ height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a u/ *: gkyfe v.uhny41zcircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative t1nu*yke:g zvy/4h fu.o Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical;kmc+t (zvgo/ spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m,m (c/t;k+ govz and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a/dr 7ib *v:kxrbwbi)p sa 3jqs.m10 o8 circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of t8dbxi7b p3/ *a k.o )rwrs:isj0mq1bvhe satellite?    s ~    min

  At what horizontal velocity would a satelli3 oh-1r 38gli/bbfm wwj.va0a te have to be launched from the top of Mt. Everest to be pl03r f1 l8 mgawb hv.oji3b-wa/aced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t;r cycb43 0vjehjbvy4cc ;0r3 ee Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Thmdu :tncq e 3d76rlgc )*w vxmn6,+oja,w3n2ze inner ram2nj3c n 6l)g at+7:dcv,qm3,rwoeuxn*dz w 6dius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotbrz3 h;1 )c ;rynyd8+pmkfa1n-hpg5e ates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s ar 53mg e )-f;kha8cd1 zhy; p+brnyp1npparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km frfic; wx 8tx dp4 nf41eniq/0(/elon k/om the center of the Earth's Moon in a space vehicle (a) moving at constaqn e/(/ po4e1n4x;/ kitdxif80wl fncnt velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two wo ae 37j:9.7 )vpzizctwa;n t ,zfm2zstars of equal mass. They are observed to be s3tzwiwz2azfjvp7a t9no;.c :7,m e)zeparated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kgr8)r5f)frx pye x:q0a woman in an elevator that x85)xpr)e: fr fayr0qmoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an ele 6)q6oq x0r8mk o1+7kp 7 gnufsqxoow0gx :4ttvator. The cor)x6 7toso6t1 n0q0q mw:po k+k8x7 xro4gfq gud can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfacetbqo0oh;bz5,l+n 8 uf of a planet with period T , the density (mass/volume) l5 8 hqbo0; tf,nub+ozof the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period ofno0f;0m :a5 pvo,;urfyty/ yx the Moon (27.4 d) to determine the period of an artificial satellite orbiting veryyo; fa0 vny/to,5fprymx0: ;u near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acdd.k7wtrs-d:b(qtp/ ross, orbits the Sun like the planets. Its period is 410 d. What (pt qr:d.-db /tkwd7sis its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis37i /sbyh1 smj 6wihv4s .hzv9gpyq 70tance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years.t , zuc mh65zd)txj4k0 It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Su)mz0hu4tjc6,tkx z5d n. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thez1ezr60 ,ujh u center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean disxuac, i90l/5mr kt7+)1pjr7ldapmr txd(o6 ftance for the four largest moons of Jupiter (those discoveredm)k,7umr6pp1t(7 xr0xadj / a dci5tlr9of +l by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Eart mp4vj,5dp b6au9vcvfin 228(:k-y e vizjqq:h from the known period and distance of the Moon. 8qiv2p9k u42 fzqn-id,j5e v jva v:(:b6cmpy    $\times 10^{24}$

  Determine the mean distance from Jupitkfst c-ru9 .:zer for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tu 9fk-:cr. ztsable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupi ja59e+hf dg:o v00aluter consists of many fragments (which some space scientists thinkd5j 0afa e hg+0ov9u:l came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale descrijg zp6li um l-(:etrn6ug:+0lozr;: cbes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Eart-u+irgn g zcztj0pu(: :lr ;m:oe6l6lh-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in izs8p5 b9r9r dnoai 5fx++rn .an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 +i +rrf.ax9dznn b8 s9orpi55 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whatf8u nz,e/kdvs j 7;q*z it is on the surfacesuz7*,k/ ; eqz n8fdjv?    $\times 10^6$

  On an ice rink, two skaters *l,.k .;ll1ox uoxwztof equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard l, oz*u. ll.w ot;kxx1are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparexiz oi uyou -4(ns 7m*e.t(cy1nt acceleration of gravity at the equator is slightly less than it would be if the Earth (y uxc( *zs.t-in17omy 4oieudidn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly uqum*(v p*gh8 gv)m4ffrom the Earth to the Moon experience zero net force becauu(mg*mq gvv48 )puhf*se the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand bi3 e83 pi2cyzon a bathroom scale in an elevatorp28i3 yiezb3c , it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space sta t.n 1 y/6rjat8atlt5vtion consists of a circular tube that will rotate about its center (like a tubular bicycle tire) 6ay5lnt/ rvttj. 1a8t(Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4aa4fh0) jaqb5iso0bi y1x q/a agk/ 693).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in termhfn /; 2r:6mikijp z3js of its radius r, the acceleration due to gravity; j:r ifzn3m kjp2i/h6 at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected3w.:a9 5my+ox76nka wjmhse )wni4tm from the vertical by an 5jmewx6.7aam3y4hi tkn)s:9m+wn wo angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m isv4 vu5e tqiz25 banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely han2evzqtv5u 5i4 dle the curve?

  How long would a day be if the Earth were rotating so fast thaz3+jdq, w+: r-gtplnst objects at the equator were apparen p:zq3 wtlsg,rdn+j+- tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant diz8v gj,xlbo7k-d sf)*stance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a ca x ly-.*q4uu7rx*(qam y*dmvj.f 8courve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.yaq f-*u(c * xm7mju*yo.8xla vr4. dq5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed t5/wwudj hs: 6chat a person wouldw6ds5w :u /hjc be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced 5 ;gn8 27wzmcqtj*ruithe presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting th mtg5;2c rq8inz ju7*we core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverngr3g)kib79:oo sjesw e*: c/ ses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where wo e wg3br*jn 7eio:oskg:) c/9suld the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellitesb*p)kjoa1vs 6k8y - wd orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each savw*)sojka1 -86pb ykdtellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), af gn hvwra1;tk5nd.6x v/84m jimc:d8jter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros j8 8kjwdx41:ct/v mhn5 .gmdvanr 6;iis roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in thj 6(cyeozu:(ae space shuttle pursuing a satellite in need of repair. You are in a circular orbi:eojz(ay(c6 ut of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yegqooiolfp frv a29e 38: ye41he48e2xars. (a) What is its mean distance from the Sg eh829o4 4eeo3yi2ox1 perfa8:qvlfun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G wouldnsr 0hfsgjj*mxt,xx *s-1k kob8/ +k* need to be if you could actually "feel" yourself gravitationally attracted to someone ne *ks*rnoxhj s1*,s -b/xgf tm8+k0kxjar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at7f04 flfg- wull u:io7 a distance of about 3o7-0lug7lwlfu i4f:f0,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses ar 6a n/.hvws,ere located at the corners of a square 0.50 m on each side. Find/,ea shr6nwv . the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg 8+dw b2l9 i*zu7unrd lz z2ww1orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration ex9z44r9 hla 1dvy d- gssvym:s6perienced by the tip of the 1.5-cm-long sweep second hand ons9vd4l91 sm:hd64 ra -vsyzyg your wrist watch?    $\times 10^{-4}$

  While fishing, you get borkbhq b.v-v)z0 ed and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angz qv)b-v0b.h kle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so c)fw ygb-ywfw 0g+ +8tthat a car traveling at speed f 8gc-b t+ww) ygf+y0w$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, t n+px5a6q hal1he Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted o+5qapn6ahlx1 n the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$